This paper presents an exact solution and an approximate solution, using the expansion of transient wave functions in a series of eigenfunctions, for the transient response of an infinitely long and multilayered circular cylinder subjected to uniformly distributed dynamic pressures at the boundaries. Numerical results are given to illustrate the effects of the layer properties on the interfacial stresses and the spatial and temporal variations of the displacement and stresses. In particular, the exact solution is used to examine the applicability of the thin shell theories to the transient response of multilayered cylinders.
Issue Section:
Technical Papers
1.
Noor
, A. K.
, and Burton
, W. S.
, 1990
, “Assessment of Computational Models for Multilayered Composite Shells
,” Appl. Mech. Rev.
, 43
, pp. 67
–97
.2.
Noor
, A. K.
, 1990
, “Bibliography of Monographs and Surveys on Shells
,” Appl. Mech. Rev.
, 43
, pp. 223
–234
.3.
Soldatos
, K. P.
, 1994
, “Review of Three Dimensional Dynamic Analyses of Circular Cylinders and Cylindrical Shells
,” Appl. Mech. Rev.
, 47
, pp. 501
–516
.4.
Valle
, C.
, Qu
, J.
, and Jacobs
, L. J.
, 1999
, “Guided Circumferential Waves in Layered Cylinders
,” Int. J. Eng. Sci.
, 37
, pp. 1369
–1387
.5.
Nayfeh
, A. H.
, Abdelraman
, W. G.
, and Nagy
, P. B.
, 2000
, “Analyses of Axisymmetric Waves in Layered Piezoelectric Rods and Their Composites
,” J. Acoust. Soc. Am.
, 108
, pp. 1496
–1504
.6.
Habip
, L. M.
, 1965
, “A Review of Recent Work on Multilayered Structure
,” Int. J. Mech. Sci.
, 7
, pp. 589
–593
.7.
Christoforou
, A. P.
, and Swanson
, S. R.
, 1990
, “Analysis of Simply-Supported Orthotropic Cylindrical Shells Subjected to Lateral Impact Loads
,” ASME J. Appl. Mech.
, 57
, pp. 376
–382
.8.
Chonan
, S.
, 1984
, “Response of a Pre-Stressed Orthotropic Thick Cylindrical Shell Subjected to a Pressure Pulse
,” J. Sound Vib.
, 93
, pp. 31
–38
.9.
Humphreys
, J. S.
, and Winter
, R.
, 1965
, “Dynamic Response of a Cylinder to a Side Pressure Pulse
,” AIAA J.
, 3
, pp. 27
–32
.10.
Sivadas
, K. R.
, and Ganesan
, N.
, 1993
, “Dynamic Analysis of Circular Cylindrical Shells With Material Damping
,” J. Sound Vib.
, 166
, pp. 103
–116
.11.
Nachbar
, P. M.
, 1962
, “On the Role of Bending in the Dynamics Response of Thin Shells to Moving Discontinuous Loads
,” J. Aerosp. Sci.
, 29
, pp. 648
–657
.12.
Jones
, J. P.
, and Bhuta
, P. G.
, 1964
, “Response of Cylindrical Shells to Moving Loads
,” ASME J. Appl. Mech.
, 31
, pp. 105
–111
.13.
Mangrum
, E.
, and Burns
, J. J.
, 1979
, “Orthotropic Cylindrical Shells Under Dynamic Loading
,” ASME J. Mech. Des.
, 101
, pp. 322
–329
.14.
Lindberg
, H. E.
, 1964
, “Buckling of a Very Thin Cylindrical Shell due to an Impulsive Pressure
,” ASME J. Appl. Mech.
, 31
, pp. 267
–272
.15.
Goodier
, J. N.
, and McIvor
, I. K.
, 1964
, “The Elastic Cylindrical Shell Under Nearly Uniform Radial Impulse
,” ASME J. Appl. Mech.
, 31
, pp. 259
–266
.16.
Lovell
, E. G.
, and McIvor
, I. K.
, 1969
, “Nonlinear Response of a Cylindrical Shell to an Impulsive Pressure
,” ASME J. Appl. Mech.
, 36
, pp. 277
–284
.17.
Loy
, T. C.
, and Lam
, K. Y.
, 1999
, “Vibration of Thick Cylindrical Shells on the Basis of Three-Dimensional Theory of Elasticity
,” J. Sound Vib.
, 226
, pp. 719
–737
.18.
Sva¨rdh
, P. A.
, 1984
, “Three-Dimensional Analysis of Axisymmetric Transient Waves in Hollow Elastic Cylinders
,” ASME J. Appl. Mech.
, 51
, pp. 792
–797
.19.
Chong
, K. P.
, Lee
, P. C. Y.
, and Cakmak
, A. S.
, 1969
, “Propagation of Axially Symmetric Waves in Hollow Elastic Circular Cylinders Subjected to a Step-Function Loading
,” J. Acoust. Soc. Am.
, 49
, pp. 201
–210
.20.
Heimann
, J. H.
, and Kolsky
, H.
, 1958
, “The Propagation of Elastic Waves in Thin Cylindrical Shells
,” J. Mech. Phys. Solids
, 14
, pp. 121
–130
.21.
Fitch
, A. H.
, 1963
, “Observation of Elastic-Pulse Propagation in Axially Symmetric and Nonaxially Asymmetric Longitudinal Modes of Hollow Cylinders
,” J. Acoust. Soc. Am.
, 35
, pp. 706
–708
.22.
Kley
, M.
, Valle
, C.
, Jacobs
, L. J.
, Qu
, J.
, and Jarzynski
, J.
, 1999
, “Development of Dispersion Curves for Two-Layered Cylinders Using Laser Ultrasonics
,” J. Acoust. Soc. Am.
, 106
, pp. 582
–588
.23.
Rabern
, D. A.
, and Lewis
, M. W.
, 1992
, “Two and Three-Dimensional Simulations of Moving Pressure Fronts in Gun Tubes
,” ASME J. Pressure Vessel Technol.
, 114
, pp. 181
–188
.24.
Cinell
, G.
, 1966
, “Dynamic Vibrations and Stresses in Elastic Cylinders and Spheres
,” ASME J. Appl. Mech.
, 33
, pp. 825
–830
.25.
Gong, Y. N., and Wang, X., 1991, “Radial Vibrations and Dynamic Stress in Elastic Hollow Cylinders,” Structural Dynamic: Recent Advances, Elsevier Science Publications, Elsevier, London, pp. 137–147.
26.
Wang
, X.
, and Gong
, Y. N.
, 1992
, “An Theoretical Solution for Axially Symmetric Problem in Elastodynamics
,” Acta Mech. Sin.
, 7
, pp. 275
–282
.27.
Wang
, X.
, 1995
, “Thermal Shock in a Hollow Cylinder Caused by Rapid Arbitrary Heating
,” J. Sound Vib.
, 183
, pp. 899
–906
.28.
Cho
, H.
, Kardomateas
, G. A.
, and Valle
, C. S.
, 1998
, “Elastodynamic Solution for the Thermal Shock Stresses in an Orthotropic Thick Cylindrical Shell
,” ASME J. Appl. Mech.
, 65
, pp. 184
–193
.29.
Yin
, X. C.
, 1997
, “Multiple Impacts of Two Concentric Hollow Cylinders With Zero Clearance
,” Int. J. Solids Struct.
, 34
, pp. 4597
–4616
.30.
Yin
, X. C.
, and Wang
, L. G.
, 1999
, “The Effect of Multiple Impacts on the Dynamics of an Impact System
,” J. Sound Vib.
, 228
, pp. 995
–1015
.31.
Wang
, X.
, and Gong
, Y. N.
, 1992
, “An Elastodynamic Solution for Multilayered Cylinders
,” Int. J. Eng. Sci.
, 30
, pp. 25
–33
.32.
Wang
, X.
, 1993
, “Stress Wave Propagation in a Two-Layered Cylinder With Initial Interface Pressure
,” Int. J. Solids Struct.
, 30
, pp. 1693
–1700
.33.
Eringen, A. C., and Suhubi, E. S., 1975, Elastodynamics, Vol. 2, Linear Theory, Academic Press, New York.
34.
Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
35.
Gurtin, M. E., 1984, “The Linear Theory of Elasticity,” Mechanics of Solids, C. Truesdell, ed., Springer-Verlag, Berlin, II, pp. 1–295.
36.
Liu
, G.
, and Qu
, J.
, 1998
, “Transient Wave Propagation in a Circular Annulus Subjected to Transient Excitation on Its Outer Surface
,” J. Acoust. Soc. Am.
, 104
, pp. 1210
–1220
.37.
Titchmarsh, E. C., 1962, Eigenfunction Expansions, Part I, Oxford University Press, London.
Copyright © 2002
by ASME
You do not currently have access to this content.
